Redundant Actuator Trajectory Control via Filtering
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Solution Overview
Problem
Managing redundant actuators in machines with redundant axes is challenging due to the complexity of reverse kinematics and the need to optimize redundant degrees of freedom for improved performance, particularly in systems with non-linear relationships and under-determined equations.
Innovation Solution
A method involving trajectory interpolation, filtering, and calculating difference trajectories between systems to effectively manage redundant axes, allowing for efficient uncoupling and optimization of movements, thereby enhancing the performance of machines with redundant kinematics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If redundant actuators are used to improve system flexibility and avoid collisions, then the ability to comply with workspace constraints and execute trajectories without collisions is improved, but the complexity of managing redundant degrees of freedom and solving under-determined equations increases
Solution Approach 1:
The control method segments the trajectory management by separating the command sequence into individual axis trajectories. Each redundant axis is controlled independently through filtering operations, dividing the complex redundant control problem into manageable single-axis sub-problems that can be solved sequentially rather than requiring simultaneous solution of under-determined equations.
Solution Approach 2:
The invention applies filtering operations to trajectories in advance before execution. By pre-processing the command sequences through filtering that anticipates constraints and singularities, the system prepares collision-free paths and avoids problematic configurations before they occur, rather than reacting to issues during real-time execution.
2Productivity
If filtering is applied to trajectories to optimize performance, then the uncoupling of trajectories and optimization of redundant degrees of freedom is improved, but the computational processing time increases
Solution Approach 1:
The filtering operation is applied separately to each axis trajectory rather than processing the entire multi-dimensional trajectory simultaneously. This segmentation of the filtering process reduces computational complexity at each step, allowing optimization of redundant degrees of freedom through sequential single-axis filtering operations.
3Speed
If the Jacobian equation is solved for redundant operating machines, then the speed of joints can be determined, but the under-determined nature of the equation requires additional homogeneous solutions that complicate the control
Solution Approach 1:
The method determines joint speeds by differentiating the forward kinematic equation beforehand, establishing a direct relationship between terminal member speed and joint speeds. This preliminary derivation avoids the need to solve under-determined Jacobian equations during real-time control, as the speed relationship is pre-established through differentiation.
Data Source
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AI summary
A method for managing systems provided with redundant actuators of the type comprising at least a first system (3, 5) operating according to a first set of variables, representative of a physical quantity to be controlled (X, Y) and a second system (17) operating according to a second set of said variables, representative of a physical quantity to be controlled (u, v), said first set of variables (X, Y) and second set of variables (u, v) identifying one or more redundant variables, said method comprising the operations of commanding said actuators (13, 14) of said system through a numeric control unit (50) and a servo control module (53) to follow trajectories of said variables ((Xs, Ys), (X, Y), (u, v)) as a function of a set sequence (P). According to the invention, said method comprises the operations of: interpolating (100) said sequence (P) to obtain a trajectory of the system with redundant actuators ((Xs, Ys)), operating a filtering (110) on said trajectory of the system with redundant actuators ((Xs, Ys)) to generate a trajectory of the first system ((X, Y)), calculating (120) a second trajectory of the second system ((u, v)) as difference trajectory between said trajectory of the system with redundant actuators ((Xs, Ys)) and said trajectory of the first system ((X, Y)), providing (130) said trajectory of the first system ((X, Y)) to said servo-control (53) for the actuation of the first system (3,5).